This report summarizes our research performed under NASA Grant NAG5-11857. The three-year grant have been supported by the Geospace Sciences SR&T program. We have investigated the energetic metastable oxygen and nitrogen atoms in the terrestrial stratosphere, mesosphere and thermosphere. Hot atoms in the atmosphere are produced by solar radiation, the solar wind and various ionic reactions. Nascent hot atoms arise in ground and excited electronic states, and their translational energies are larger by two - three orders of magnitude than the thermal energies of the ambient gas. The relaxation kinetics of hot atoms determines the rate of atmospheric heating, the intensities of aeronomic reactions, and the rate of atom escape from the planet. Modeling of the non-Maxwellian energy distributions of metastable oxygen and nitrogen atoms have been focused on the determination of their impact on the energetics and chemistry of the terrestrial atmosphere between 25 and 250 km . At this altitudes, we have calculated the energy distribution functions of metastable O and N atoms and computed non-equilibrium rates of important aeronomic reactions, such as destruction of the water molecules by O(1D) atoms and production of highly excited nitric oxide molecules. In the upper atmosphere, the metastable O(lD) and N(2D) play important role in formation of the upward atomic fluxes. We have computed the upward fluxes of the metastable and ground state oxygen atoms in the upper atmosphere above 250 km. The accurate distributions of the metastable atoms have been evaluated for the day and night-time conditions.